derivative p(x)=(x-3)^3-(x-2)^2+31

Lösung

ableitung von

p (x) = (x - 3)^{3} - (x - 2)^{2} + 31

3 x^{2} - 20 x + 31

Schritte zur Lösung

\frac{d}{d x} ((x - 3)^{3} - (x - 2)^{2} + 31)

Vereinfache

(x - 3)^{3} - (x - 2)^{2} + 31 : x^{3} - 10 x^{2} + 31 x

= \frac{d}{d x} (x^{3} - 10 x^{2} + 31 x)

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (x^{3}) - \frac{d}{d x} (10 x^{2}) + \frac{d}{d x} (31 x)

\frac{d}{d x} (x^{3}) = 3 x^{2}

\frac{d}{d x} (10 x^{2}) = 20 x

\frac{d}{d x} (31 x) = 31

= 3 x^{2} - 20 x + 31

\int_{\frac{1}{2}}^{1} \frac{x + 4}{x ^{2} + x} d x

\int_{0}^{1} \int 1 d x d y

x \to 4 lim (x + 2)

\int_{1}^{8} π (x - 1) d x

t an g e n t f (x) = 3 x^{2} + 8 x + 4, at x = - 1